A common component of investing money is to take advantage of a financial institution’s willingness to pay compound interest. Compound interest is basically interest paid on a deposit that continually accumulates interest. In general, the formula for compound interest can be represented by the following exponential function:

In this formula, P(t) represents the total money in the account after t years given the interest rate k which is compounded continuously. In this assignment, you will use this formula to explore the affect that compound interest can have over a period of time and at different interest rates.

Directions:

- Select an amount of money that you would like to invest (for example $1000.00). This will be your P
_{0}value. - Let your interest rate be k = 0.5%.
- Write out the exponential function using the P
_{0}and k values you have. - Determine the value of your investment after 1, 5, and 10 years.
- Now, find the doubling time T for your investment. In other words, at what time would your initial deposit double in value?
- Repeat steps 3 through 5 for k = 1%.
- Repeat steps 3 through 5 for k = 1.5%.

In a Microsoft Word document, prepare a report that includes answers to the following:.

- Report the results of the calculations you performed above.
- What affect did changing the interest rate have on the rate at which your investment grew?
- What affect did changing the interest rate have on the doubling time (time until your initial deposit doubled in size)?
- Assume that this money is being invested in a savings account. Are the interest rates we selected realistic for such an account today?
- Consider the formula we used to determine the future value of our deposit. Is this formula a realistic approximation of what we could expect from an investment or are there other issues or factors that must be considered?
- Besides savings accounts, what other kinds of investment accounts or programs are typically offered at your bank? Do these accounts use compound interest? What are the typical interest rates for these accounts?
- Use your textbook or another reference to research how to calculate simple interest. Given what you know about compound and simple interest, which would you prefer that your investment programs were based upon? Why?